Transient characteristics of the rectangular latent heat storage vessel packed with shape-stabilized phase change (solid-liquid) material (PCM) are investigated numerically
by solving the governing equations of both the PCM and the heat transfer medium(water) simultaneously as a conjugate problem with the finite difference technique. It's found that the heat storage characteristics are greatly affected by the flow direction of the heat transfer medium since the natural and forced convection coexists in the heat storage vessel. That is, it is classified that the effectively thermal efficiency of the latent heat storage system is obtained by the downflow along vertical PCM for heat storage process and the upflow for heat release process. The effect of the inlet velocity of heat transfer medium(water) on transient heat characteristics of the latent heat storage system is also revealed in the present study

Inaba, Hideo

Ozaki, Koichi

Tu, Ping

English

Okayama University Scientific Achievement Repository

Memoirs of the Faculty of Engineering,Okayama University,Vol.29, No.2, pp. 5 -12, March 1995Numerical Study on Transient Heat Characteristicsof a Rectangular Latent Heat Storage VesselHideo INABA*, Ping TU** and Koichi OZAKI*(Received January 27 , 1995)Transient characteristics of the rectangular latent heat storage vessel packed withshape-stabilized phase change (solid-liquid) material (PCM) are investigated numeri-cally by solving the governing equations of both the PCM and the heat transfer me-dium(water) simultaneously as a conjugate problem with the finite difference techni-que. It's found that the heat storage characteristics are greatly affected by the flowdirection of the heat transfer medium since the natural and forced convection co-exists in the heat storage vessel. That is, it is classified that the effectively thermalefficiency of the latent heat storage system is obtained by the downflow along verti-cal PCM for heat storage process and the upflow for heat release process. Theeffect of the inlet velocity of heat transfer medium(water) on transient heat charac-teristics of the latent heat storage system is also revealed in the present study.1 INTRODUCTIONThe latent heat storage systems are widely utilized to consume energy efficiently and economically. Asa specific application, using the off-peak electric power during the midnight, the heat can be stored intothe latent heat storage material economically. The stored energy is used during the day time avoiding theperiod of the peak electric power demands. Therefore, for this type of heat storage system, the shortertime that the heat storage process takes and the higher output temperature of the heat transfer mediumduring the heat release process should be desirable. A new type of PCM(l) that consists of the shape-stabilized paraffin dispersed within the polyethylene as the basic material is utilized in the present heatstorage system. It is an attractive heat storage material which keeps its shape even if the paraffin as thePCM melts completely, since the PCM can contact with the heat transfer fluid directly without the heatresistence.The rectangular heat storage vesselis composed of a number of rectangularcross-sectioned channels for the heat trans-fer medium arranged in paralled and sepa-rated by the PCM as shown in Fig.I. Asthe arrangement of all the channels andheat storage section is identical and theeach heat transfer medium flow rate inthe channels is equal, the analysis canthus be restricted to the consideration ofa section composed of only one-half of thechannel and the PCM as shown in Fig.2.When the inlet velocity of the heat transfermedium is in the direction of the gravity,the calculating model is called the down-flow model. Otherwise, it is called theupflow model.Fig.1 The schematic of the heat storage unit* Department of Mechenical Engineering** Graduate School of Okayama University56 Hideo INABA, Ping TU and Koichi OZAKI2 NOMENCLATURE--''---~O---t-:----'''''''i--'_--L._--+X (U)In OutFig.2 The analysing model( cross sectionof the heat storage unit,not scale)Upflow modelDownflow modelL: 1000mmL1:50mmL2:50mmW1: 7mmW2: 5mm~iDEE~oQ)c::JW2"~"FluidY MOuttW1I~iD VEE>-Ul I0 peMQ)c::J....JC: specific heatCpe: equivalent apparent heat capacityL: length of the heat storage unitP: pressureT: temperatureTout: outlet bulk temperatureU, V: velocityWI: half width of PCMW2: half width of the flowing channelx, y: coordinate directionsGreek Symbolsp: densityr: timep: dynamic viscosityA: thermal conductivity(3: volume expansion coefficientat constant pressureSubscripts0: initial conditionin: inletout: outlet3 MATHEMATICAL MODELINGThe continuity, momentum, and energy conserving equations of two-dimensional transient incompress-ible laminar flows are as follows:• continuity equationau ov-+-=0ox oy (1)• momentum equationsAU au au-+u-+v-at ox oyov ov ov-+u-+v-at ox oy= V (02U + 02U ) _ ~ oPox2 oy2 p oxdiv(vgrad V) - ~ oP _ 9pay(2)(3)• energy equationo(pCpeT) o(PCpeT ) o(pcpeT) d' (\ d T)at . +u ox + v oy = W /\ gra (4)In equation(3), Boussinesq approximation is applied, that isFor the PCM, the c in the energy equation is written as Cpe, and the Cpe is the equivalent apparent heatcapacity, If there is no phase change, the Cpe is equil to the apparent heat capacity. When the phasechanges, the Cpe includes both of apparent heat and latent heat of the PCM, and the relationship betweencpe and temperature is derived from the measured results of the shape-stabilized PCM by using DSC(1).The initial and boundary conditions for the case of uniform inlet conditions are defined as follows:• initial conditiont=O u = v = 0 , T = To (5)Numerical Study on Transient Heat Characteristics of a Rectangular Latent Heat Storage Vessel• boundary condition for velocity7{X = Ommy=Ommx = 12mm• boundary condition for temperature~=Ov = Vin8v - 0(JX-u=Ou=Ou=O(6){X = Ommy=Ommx = 12mm4 NUMERICAL PROCEDUREi-=OT = Tini- =0(7)The solution procedure used for solving the above equations is the control-volume finite-difference ap-proach described by Patankar(2). In this methodology, the domain is discretised into a number of controlvolumes (each associated with a nodal point)such that some control volume faces coincide with the PCM-heat transfer medium(water)interface. The pressure-velocity interlinkage is handled by using SIMPLEscheme(2). The converged results for velocity and pressure are assumed to be reached on these conditionsthat are the sum of the residuals of the continuity equation is less than 10-8 and the maximum of theresiduals is less than 10-5 • Furthermore, the iteration for temperature 'is continued until the sum of theresiduals of energy conserving equations is less than 10-4 and the maximum relative change of temperaturebetween consecutive iterations is less than 10-4 . For every time step, the calculation is also checked byobserving the energy balance in the whole solution domain. Results show the sum of the heat releasedfrom(or the heat stored in) the PCM, and the heat transfer mediuni(water) is eaual to the whole enthalphydifference between the inlet and outlet heat transfer medium within the range of ±0.1%5 NUMERICAL RESULTS AND DISCUSSIONThe geometrical variables keep at constant values of L = 1m, WI = 7mm, and W2 = 5mm in thepresent analysis. The PCM and the heat transfer medium(water) are initially static and at the sameinitial temperature To . At the entrance in width of (WI +W2) , the heat transfer medium has a uniformtemperature distribution (Tin) and uniform velocity distribution (Vin) .5.1 Comparison of the Numerical Results with the Experimental OnesAt first the above equations and numerical procedures were checked against experimental results . Asshown in Fig.3 , in the heat storage process, the heat transfer medium flows down as shown in Fig.2.Comparing the calculated outlet bulk temperature Tout of the heat transfer medium with that measured,it can be seen that the present numerical result agrees well with the experimental one.Tout2ExperimentI~~t-'------------CalculationTin~1.4·CVin=4,2mm/sTO=28.0·CTout---o 1000 T [sec]Fig.3 Comparison of the numerical result with experimental one8 Hideo INABA, Ping TU and Koichi OZAKIIn order to investigate the effect of flowing direction for the heat storage and heat release processes, thenumerical computations of both upflow and downflow model for different process are conducted.5.2 Heat Storage CharacteristicsFor the heat storage process, when the inlet velocity Vin , the inlet temperature Tin and the initialtemperature of the rectangular heat storage vessel To equal 1.6mm/sec, 60 °e,45 °e respectively, thenumerical results of upflow model are given in Figs.4 and 5. Under the same calculating conditions, thenumerical results of downflow model are shown in Figs.6 and 7. As shown in Fig.4, the temperature of theheat transfer medium close to the PCM (x = WI) is lower than that of near the centerline (x = WI +W2).Therefore the density of the heat storage medium near the PCM is larger. As a result, natural convectionoccurs and causes the heat transfer medium near the PCM to flow against the upflow of forced convection.On the other hand, for downflow model, as shown in Fig.6, the velocity profile has a quite differentshape against that in Fig.4 , and the heat transfer medium near the PCM is accelerated by the naturalconvection near the PCM. Therefore, the heat transfer between the PCM and the fluid is enhanced in thiscase, contrasting to the upflow model. Comparing the melting fronts between Fig.5 and Fig.7 at differenttimes, the melting fronts for downflow model moves faster than that of upflow model due to ascendingflow near the PCM by natural convection. It can be seen that the downflow can meet the demand ofshortening the heat storage period.5.3 Heat Release CharacteristicsFor the heat release process, when the inlet velocity Vin , the inlet temperature Tin and the initialtemperature of the rectangular heat storage vessel To are equal to 1.1mm/sec, 45 OC, 60 °e , respectively.The numerical results of upflow model are given in Figs.8 and 9 . Under the same initial and boundaryconditions, the numerical results of downflow model are given in Figs.10 and 11. The temperature ofthe heat transfer medium(water) near the PCM is higher and its density is smaller than those of theheat transfer medium close to the centerline (x = WI + W2) . As indicated in Fig.10, the heat transfermedium near PCM changes its flowing direction, and the heat transfer medium close to the centerlineis accelerated considerably as the total mass flow is fixed. Therefore the output bulk temperature Toutfalls down immediately after the heat release process begins. Because for the specific application in whichthe high output bulk temperature is desirable, the above case should be avoided and the upflow model isfavorable as in this case the output bulk temperature Tout can keep relatively higher value for a long timeas shown in Fig.12.The inlet velocity of the heat transfer medium is also an important factor to know the characteristics ofthe rectangular heat storage vessel besides of flowing direction. The effects of inlet velocity are illustratedin Figs.13, 14 and 15. The 71 is the finishing time of the heat storage process or heat release process.Fig.13 shows that for the heat storage process and downfl.ow model, the larger the inlet velocity of heatstorage medium, the shorter the heat storage time. On the other hand, for heat release process and upflowmodel, as shown in Figs.14 and 15, as the inlet velocity of the heat transfer medium decreases, the timeto finish the whole process increases and higher output bulk temperature can be gained.6 CONCLUSIONA rectangular heat storage vessel with the configuration in Fig.1 has been studied numerically. Theobtained results show that the flowing direction and inlet velocity of heat transfer medium influence itstransient characteristics significantly. In order to meet the demand of the specific application, downflowingand larger inlet velovity of the heat transfer medium is satisfied for heat storage process, and for heat releaseprocess, upflowing and smaller inlet velocity is suitable. This conclusion provides guidelines for the designof the heat storage unit. More extensive parametric investigation is due to be continued.References[1] H.Inaba et al., 15th Jap. Symposium on Thermophysical Properties, (1994) ,pp.211-214.[2] S. V. Patankar , Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York (1980).Numerical Study on Transient Heat Characteristics of a Rectangular Latent Heat Storage Vessel 920c:>:>104min.12min. ------20min. ---28min. ----40min. - - --10--PCM--"------",,".. '" /-". ""-- ,.,-- ".'"---o~Ic.=::::::~IC.0.50.01 X (m)FigA Temperature distribution and streamwise velocity distribution at y=550mm(the thick line: temperature; the thin line: velocity;heat storage process,upflowing)Q)<II.~E ~::!E III .~l!!0 Ci5 c'5c-'0Q) it~~QiEE>.enFig.5 PCM's melting fronts with time T(heat storage process, upflowing)1000sec. - - -800sec.1884sec. - - -1500sec. - - --500sec.FLUID______ .- - c..... ------ 5"---- >-,....:--- -:"",. - - - - - - 4.. ':::.'~----'""""IPCM---~ICt::--'0l-IC.0.5L..-....L.--IL..-....L.---I'--....L..----I_.......--L_....L......"....a,...,.....................J 0o 0.01 X (m)Fig.6 Temperature distribution and streamwise velocity distribution at y=550mm(the thick line: temperature; the thin line: velocity; heat storage process, downflowing)10 Hideo INABA, Ping TV and Koichi OZAKI(])(J):::E'~ ~u 3l '~Q.. ~~0CD11Jii~a;EE~Fig.7 PCM's Freezing fronts with time T(heat storage process, downflowing)500sec.3000sec. - - - -1000sec. - - - - -~--'-;~~-=l2 2000sec. - - ------ 0PCM......------............---------.--o"2.=I~--c.=IC0.5Fig.8 Temperature distribution and streamwise velocity distribution at y=550mm(the thick line: temperature; the thin line: velocity; heat release process, upflowing):::E CDU (J)Q..'3'0 E ~CD al .~:§ ~~ en (!Ja;11EE>-(J)Fig.9 PCM's freezing frontswith time T(heat resease process, upflowing)Numerical Study on Transient Heat Characteristics of a Rectangular Latent Heat Storage Vessel 114000sec.2000sec. - - -500sec.1000sec.3000sec.c5":>o10....- -----c'7~0.8t- _C.=- -----I ......C. .........OL.----------'------_--J -10Fig.10 Temperature distribution and streamwise velocity distribution at y=550mm(the thick line: temperature; the thin line: velocity; heat release process, downflowing)Q)VJ::E .~() E ~a. Ol .~'5 ~OJ en C!l~11~1iiEE>-enFig.11 Freezing fronts for various time periods(heat release process, downflowing)6050Upflowing - - - - -Downflowing4000T (sec.)Fig .12 The outlet bulk temperature for different flowing direction(heat resease process)12 Hideo INABA, Ping TV and Koichi OZAKI.....,.. 3000<.JOJ~J-200010001..-...J....-J..-J.....J......L....L--__..L-_--L_....J...---JL.......J1. 2. 3. 4. 5.Vin(mm/sec.)Fig.13 The variation finishing times with inlet velocity(heat storage process,downflowing)20000Vin(mm/sec.)2000 L..L....... -'-_-'---I.---l--l.-I...................__---'"'2.04000300010000Fig.14 The finishing time for various inlet velocities(heat release process, upflowing)• Vin=1.1 mmlsec.o Vin=O.5 mm/sec.o Vin=O.1 mmlsec.605040o 10000 T (sec.) 20000Fig.15 The outlet bulk temperature for various inlet velocities(heat release process, upflowing)

Numerical Study on Transient Heat Characteristics of a Rectangular Latent Heat Storage Vessel

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